In the limit of \(n \rightarrow 0\)  and \(\tilde{Q}_{m,c} \rightarrow 0\) , eqs. (REF ) and (REF ) are reduced to \(T_c=\sqrt{\frac{2}{3}}\frac{1}{\pi \ell }\) , \(S_c=\frac{\pi C}{6 }\)  and \(\tilde{Q}_{e,c}=\frac{C}{6}\)  which present the Resener-Nordstrom black holes in the RPS formalism [1]}.
Also, the Helmholtz free energy is given by
\(F(T,\tilde{Q}_e,\tilde{Q}_m,C)=M(S,\tilde{Q}_e,\tilde{Q}_m,C)-TS.\) 
